KL-SN [1]} uses a more sophisticated exploration rate so as to avoid a naïve union bound over time. We first find \(\gamma > 1\)  that satisfies the following equation, and thereafter set the exploration rate as given below.
\(2e^2\gamma e^{-\gamma } = \alpha \text{ and } \beta (t, \alpha ) = \frac{\gamma (1 + \text{ln}(\gamma ))}{(\gamma - 1)\text{ln}(\gamma )} \text{ln(ln}(t)) + \gamma .\) 
